Bonn Topology Group - Abstracts

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Talk

July 7, 2026
Filippos Sytilidis (MPIM Bonn): Towards a finite presentation of the 3-dimensional bordism bicategory

Abstract

Topological quantum field theories (TQFTs) are symmetric monoidal functors from bordism categories to categories of vector spaces. Classifying low-dimensional TQFTs often relies on presenting bordism categories in terms of generators and relations. This talk introduces these ideas and outlines a general procedure, due to Juhász, for constructing such presentations using Morse–Cerf theory and surgery. We further discuss how this perspective can be extended to yield presentations of bordism bicategories and describe an explicit finite presentation of the invertible part of the 3-dimensional bordism bicategory, following joint work with Bruce Bartlett and Chris Douglas.

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